Emergence and Stability of a Hybrid Lamella–Sphere Structure from

Letter Cite This: ACS Macro Lett. 2018, 7, 95−99

pubs.acs.org/macroletters

Emergence and Stability of a Hybrid Lamella−Sphere Structure from Linear ABAB Tetrablock Copolymers Bin Zhao,† Wenbo Jiang,† Lei Chen,† Weihua Li,*,† Feng Qiu,† and An-Chang Shi‡ †

State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China ‡ Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada S Supporting Information *

ABSTRACT: The self-assembly of linear A1B1A2B2 tetrablock copolymers is studied using the self-consistent field theory, aiming to target the formation of stable hybrid structures composed of lamellar and spherical domains of the same component, i.e., the lamella−sphere (LS) phase. Two types of lamellar morphologies, regular (L) and sandwich-like (L′), are observed, and their transition is identified as firstorder. The formation of L′ is a prior condition for the formation of LS because the disordered short A2-blocks sandwiched in the B domain in L′ aggregate into spheres as χN increases, leading to the formation of LS. The separation of A2-blocks from A1-blocks in L′ or LS causes extra interfacial energy, which is compensated by the gain of configurational entropy. The tail B2-block is demonstrated to play a critical role in enlarging the gain of configurational entropy. In a word, the formation of L′ is driven by entropy, while the transition from L′ to LS is driven by enthalpy.

T

the AB diblock copolymer, their phase boundaries are significantly shifted.10 A typical example is the linear ABA triblock copolymer,24 which could be obtained by adding an additional A-block onto the end of the B-block of the AB diblock. In particular, for asymmetric A1BA2 with τ = NA2/(NA1 + NA2), where NA1 and NA2 indicate the number of statistical segments of A1- and A2-blocks, respectively, interesting phase re-entry like L → G → C → G → L as τ increases for fixed volume fraction was observed, which has been confirmed by very recent experiments.33 This observation demonstrates the important role of architecture as an additional factor to the volume fraction and the interaction parameter even for linear AB-type block copolymers. Nevertheless, most of the structures in AB-type block copolymers consist of only one type of geometry of minority domains, such as sphere, cylinder, or lamella, while stable hybrid structures containing different geometries are rarely reported. For example, lamellar and spherical domains are formed simultaneously with the same chemical component, referred to as the hybrid lamella−sphere (LS) phase. Note that this kind of hybrid phase is capable to produce lines and dots simultaneously, thus having a promising application perspective in block copolymer lithography.5 Recently, the LS phase was observed in highly asymmetric A1BA2 triblock copolymers by Monte Carlo (MC) simu-

he self-assembly of block copolymers has attracted longlasting interest due to its remarkable ability of forming rich ordered nanostructures that exhibit promising potential applications in a wide range of fields.1−5 Though it is easy to understand that the general mechanism that block copolymer self-assembly is governed by the competition between the interfacial energy and the entropic energy,6 it is still challenging to predict the geometry of the resulting structures. Even for the ideal model system, i.e., the simplest AB diblock copolymer, it has taken a long period to obtain the relatively complete phase diagram under the concerted interplay of theory and experiment,7 which consists of several ordered phases: hexagonally close-packed (HCP) and body-centered-cubic (BCC) sphere, hexagonal cylinder (C), double Gyroid (G) and Fddd (O70) bicontinuous network, and lamella (L).8−10 However, recent insightful experiments observed more complex spherelike phases in some specific diblock copolymers,11−15 Frank−Kasper (FK) phases, whose stabilization mechanism was revealed by relevant self-consistent field theory (SCFT) studies.16,17 Instructively, these complex FK phases were also predicted as stable in other AB-type block copolymer systems by SCFT.17,18 On one hand, these observations confirm the difficulty with the prediction of phase behaviors. On the other hand, it implies a possibility to generate more ordered phases with AB-type copolymers by tailoring the chain architecture.19,20 The phase behaviors of various AB-type block copolymer melts have been systematically explored by SCFT.10,16,21−32 Though many of them resemble the similar phase sequence as © XXXX American Chemical Society

Received: October 17, 2017 Accepted: December 26, 2017

95

DOI: 10.1021/acsmacrolett.7b00818 ACS Macro Lett. 2018, 7, 95−99

Letter

ACS Macro Letters lations;34 however, quantitative verification of its stability is lacking. It is instructively observed by MC that short A2-blocks aggregate into spherical A-domains in the lamellar B-domain, while long A1-blocks self-assemble into the lamellar A-domain, leading to the LS morphology [Figure 1(a)].34 Intuitively, if

tetrablock A1B1A2B2, which is readily accessed by modern synthetic techniques.35,36 Hence, if a short A2-block enters the layering domain mainly composed of A1-blocks, it has to form an extra small loop in any possible configuration of A1B1A2B2 [Figure 1(b)]. To constrain the two junction points of the A2block on the A/B interface results in an entropic loss, which becomes more severe as the A2-block shortens relative to the decreasing A2/B interfacial energy. Additionally, the looping configuration of the A2-block also increases the A2/B interfacial area, which reduces the superiority of the A1/A2 blending configuration in the interfacial energy over their separation. Accordingly, here we will study the phase behavior of A1B1A2B2 melts using SCFT, focusing on the emergence and stability of the LS phase. Details of SCFT are provided in the Supporting Information. The numbers of segments on the four blocks are specified as NAi and NBi (i = 1 and 2), respectively, with NA1 + NA2 + NB1 + NB2 = N, fAi = NAi/N, f Bi = NBi/N, fA = fA1 + fA2, f B = f B1 + f B2, τA = NA1/(NA1 + NA2) = fA1/fA, and τB = NB1/(NB1 + NB2) = f B1/f B. Besides the interaction parameter, χN with χ being the Flory−Huggins parameter and N the total number of segments, three other independent variables are needed to characterize the phase behaviors, e.g., fA, τA, and τB. To give prominence to the effect of architecture, we fix the composition as symmetric, i.e., fA = f B = 0.5. As mentioned previously, one of the most attractive features in the phase behavior of asymmetric A1BA2 copolymers lies in the phase reentry as τ varies occurred for a fixed composition. This phenomenon should also occur with the phase behavior of A1B1A2B2 because of the possible separation between the two A-blocks as well as between the two B-blocks. Of course, the two re-entry phenomena for A- and B-blocks are mirror symmetric. We calculate the phase diagram of A1B1A2B2 with respect to τA and τB for fA = f B = 0.5 and χN = 60 (Figure 2).

Figure 1. Possible configurations of A1BA2 triblock (a) and A1B1A2B2 tetrablock (b) copolymers in a regular lamella or hybrid lamella− sphere (LS) morphologies: A-blocks in red color and B-blocks in blue color. The dangling A2-blocks in the B-domain are either disordered or aggregated into spheres (above or below the dashed lines).

the long A1- and short A2-blocks aggregate separately, they could form lamellae and spheres in the same morphology, respectively. The complete separation between A1- and A2blocks means that there is only a unidirectional bridging configuration (e.g., A1 → B → A2), while the other directional bridging configuration is not allowed (e.g., A2 → B → A1), which is very entropically unfavorable. The mixing bidirectional bridging configurations drive the mixing of A1- and A2blocks. In addition, looping configuration also appears in the lamellar morphology of ABA triblock copolymers,24 also causing the mixing of the two different A-blocks. No doubt, these mixing configurations lead to the formation of the regular lamellae (denoted by L). However, when the A2-block is very short, its separation from the B-domain leads to a limited gain of interfacial energy but at the expense of configurational entropy. As a result, the very short A2-block tends to be dangled in B-domain in order to access more configurations at the low expense of interfacial energy, thus increasing the effective volume fraction of Bdomain relative to its characteristic value. The probability of the dangling configuration should increase as the A2-block shortens. As the dangling A2-blocks aggregate together within the B-domain, the lamellar phase becomes sandwich-like (denoted by L′). The change of the effective volume fraction due to the swollen B-domain by the dangling A2-blocks governs the phase re-entry. At the same time, the dangling A2blocks could aggregate into spherical domains to reduce the A2/B interfacial energy as long as the local segregation between them and B-blocks is high enough. In a word, LS could be formed when the sandwiched A2-blocks aggregate into spheres before the layering A-domain transforms into the cylinder as its effective volume fraction decreases. In contrast to the regular L phase, the separation of A1- and A2-blocks in L′ increases the interfacial energy. L′ becomes stable over L if and only if the gain of entropy can compensate the loss of interfacial energy. In other words, the formation of L′ is driven by entropy, while its transition to LS is driven by enthalpy. Our later SCFT calculations will demonstrate that L′ as well as LS is hard to be stabilized in A1BA2 due to the limited gain of entropy. To enhance the gain of entropy from the separation of A1- and A2-blocks, we purposely attach an additional B-block to the end of the A2-block, forming a linear

Figure 2. Phase diagram in the τB−τA plane of A1B1A2B2 tetrablock copolymers with χN = 60 and fA = f B = 0.5. The filled circles denote the phase transition points determined by SCFT, while the solid lines are a guide for the eyes.

The considered candidate morphologies are listed in Figure S1. Apparently, the phase diagram is mirror symmetric with respect to the diagonal connecting the top-left and bottomright corners, which is dictated by the exchange symmetry between A and B blocks. Interestingly, the gyroid and cylinder phases exhibit considerable stability regions besides the lamellar phases for the case of ideally symmetric composition, 96

DOI: 10.1021/acsmacrolett.7b00818 ACS Macro Lett. 2018, 7, 95−99

Letter

ACS Macro Letters giving rise to the phase re-entry as τA or τB varies. Note that the denotation Cα or Gα (α = A and B) indicates the cylinder or gyroid phase whose minority geometry is composed of an αcomponent. Without loss of generality, we focus on the phase re-entry as τA varies. The typical phase re-entry is L′ → CA → GA → L as τA decreases for 0.3 < τB < 0.85. For τA = 1, corresponding to the AB diblock, there is no doubt the stable phase is lamella. As τA decreases from 1, increasing A2-block divides the B-block into two pieces, B1- and B2-blocks. When the A2-block is short, it would stay within the B-domain instead of joining in A1blocks, thus increasing the effective volume fraction of Bblocks, f Beff > f B. The energy gain from the increased configurations when mixing short A2-blocks into the B-domain is larger than the cost of interfacial energy. As f eff B becomes adequately asymmetric, the stable phase transfers from L′ to CA. However, this increasing trend of f eff B as τA decreases cannot be maintained because the interfacial energy is continuously increased, and thus it would drive A2-blocks to leave the B-domain. Accordingly, the symmetric volume fraction is restored as more A2-blocks leave the B-domain, i.e., that f eff B decreases toward its characteristic value f B = 0.5, leading to the inverse transition from CA going through GA into L. To clearly demonstrate the variation of f eff B , we estimate its value of the lamellar phase that transforms from L′ to L as τA decreases or fA2 increases without considering the intermediate phases of cylinder and gyroid (Figure S2). When fA2 increases from 0, most of the A2-blocks stay in the B-domain, leading to a nearly linear growth of f eff B ≈ f B + fA2 = f B + (1 − τA)fA. As fA2 increases, the amount of A2-blocks joining in the major Adomain increases, finally leading to the transition from L′ to L when most of the A2-blocks enter the A-domain. Surprisingly, C for fixed τB = 0.5, f eff B abruptly drops off at a critical τA ≈ 0.77, which implies a first-order transition between L′ and L.37 In addition, the first-order transition is evidenced by their free energy comparison as well as the discontinuous variation of their domain spacing as τA increases (Figures S3 and S4). Note that L′ has a notably larger period than L due to its lower content of looping configurations. Interestingly, the first-order transition vanishes at the side of large τB where L′ and L become indistinguishable (Figure S5). In particular, for τB = 1 corresponding to the case of asymmetric A1BA2, the portion of A2 in the B-domain of L′ is vanishingly small (Figure S6). This implies that the LS phase should be hard to stabilize in asymmetric A1BA2 copolymers. Notice that the above phase re-entry exhibits an asymmetric phase sequence, L′ → CA → GA → L, which is in obvious contrast to the generic phase sequence as composition in ABtype block copolymers. In other words, the Gyroid phase only appears at the lower side of the cylinder phase in the phase region but not at the upper side. This asymmetric feature is attributed to the asymmetric change of f eff B as τA increases at the two sides of the cylinder. At the upper side with τA > 0.82, most of the short A2-blocks enter the B-domain, thus inducing an almost linear increment to f eff B as the length of the A2-block. In contrast, at the lower side, f eff B is dictated by a pair of competing factors. Although longer A2-blocks are more likely to migrate into the major A-domain by enforcing the polymer chains to adopt some looping configurations [Figure 1(b)], only a proportion of them do so because of the need to balance the loss of configurational entropy and the gain of interfacial

energy. On one hand, there is a smaller proportion of longer A2-blocks as fA contributing to f eff B . On the other hand, the increasing length of the A2-block partially compensates the lowering of f eff B. For a given τB, the local segregation degree is determined by the length of the A2-block and χN. With χN = 60, no stable LS phase is observed because short A2-blocks prefer to be disorderly dangled in the B-domain for such low segregation between A2-blocks and B-blocks. To examine the effect of χN on the formation of LS, we construct the phase diagram with respect to τA and χN for fixed τB = 0.5 and fA = f B = 0.5 (Figure 3). Surprisingly, a noticeable stability region of LS is observed

Figure 3. Phase diagram of A1B1A2B2 tetrablock copolymers in the τA−χN plane for fixed fA = f B = 0.5 and τB = 0.5.

between L and CA for χN ≳ 74. A typical comparison of free energy for χN = 80 is given in Figure S7, while the comparisons of interfacial and entropic contributions are given in Figure S8. As expected, the local aggregation of A2blocks makes LS have more favorable interfacial energy but higher entropic energy than L′ in the stability region of LS. Note that the density of A-blocks within the spherical domain of LS is much higher than that of the A-blocks sandwiched in the B-domains of L′, and it increases to become larger than 0.9 at χN = 90 (Figure S9). This observation evidences that the spherical domains of LS are well separated from the “B-matrix”. To demonstrate the key role of the B2-block on stabilizing L′ and thus LS further, we calculate the peaking densities of A2blocks (ϕPA2) within the B-domain as a function of τA for τB = 0.5 and χN = 80 and compare it with that of τB = 1 (i.e., A1BA2) (Figure S10). We find that A2-blocks of L′ locally aggregate into spheres at ϕmax A2 ∼ 0.25 for τB = 0.5, thus forming LS. In contrast, the maximum value of ϕPA2 is only about 0.07 for τB = 1, which is far below the threshold value for the aggregation of A2-blocks. More interestingly, the maximum of ϕPA2 cannot be simply increased by enhancing χN (Figure S11). This observation reveals that LS may not be stabilized in asymmetric A1BA2. There is still one question to be answered, i.e., whether other hybrid phases such as the lamella−cylinder, gyroid−sphere, and cylinder−sphere are stable. Our answer is yes if we could adjust more parameters such as χN and fA. For example, according to the transition sequence of A2-domains within Bdomains from disordered to sphere and then to cylinder, the lamella−cylinder phase might become stable in the region with χN far above the LS region. In addition, another critical 97

DOI: 10.1021/acsmacrolett.7b00818 ACS Macro Lett. 2018, 7, 95−99

Letter

ACS Macro Letters

(6) Matsen, M. W.; Bates, F. S. Origins of Complex Self-Assembly in Block Copolymers. Macromolecules 1996, 29, 7641−7644. (7) Matsen, M. W. The Standard Gausian Model for Block Copolymer Melts. J. Phys.: Condens. Matter 2002, 14, R21−R47. (8) Matsen, M. W.; Schick, M. Stable and Unstable Phases of a Diblock Copolymer Melt. Phys. Rev. Lett. 1994, 72, 2660−2663. (9) Tyler, C. A.; Morse, D. C. Orthorhombic Fddd Network in Triblock and Diblock Copolymer Melts. Phys. Rev. Lett. 2005, 94, 208302. (10) Matsen, M. W. Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts. Macromolecules 2012, 45, 2161− 2165. (11) Lee, S. W.; Bluemle, M. J.; Bates, F. S. Discovery of a FrankKaspers Phase in Sphere-Forming Block Copolymer Melts. Science 2010, 330, 349−353. (12) Gillard, T. M.; Lee, S.; Bates, F. S. Dodecagonal quasicrystalline order in a diblock copolymer melt. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 5167−5172. (13) Kim, K.; Schulze, M. W.; Arora, A.; Lewis, R. M.; Hillmyer, M. A.; Dorfman, K. D.; Bates, F. S. Thermal Processing of Diblock Copolymer Melts Mimics Metallurgy. Science 2017, 356, 520−523. (14) Schulze, M. W.; Lewis, R. M.; Lettow, J. H.; Hickey, R. J.; Gillard, T. M.; Hillmyer, M. A.; Bates, F. S. Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers. Phys. Rev. Lett. 2017, 118, 207801. (15) Takagi, H.; Hashimoto, R.; Igarashi, N.; Kishimoto, S.; Yamamoto, K. Frank-Kasper Phase in Polybutadiene-Poly(ϵ-caprolactone) Diblock Copolymer/Polybutadiene Blends. J. Phys.: Condens. Matter 2017, 29, 204002. (16) Grason, G. M.; DiDonna, B. A.; Kamien, R. D. Geometric Theory of Diblock Copolymer Phases. Phys. Rev. Lett. 2003, 91, 058304. (17) Xie, N.; Li, W. H.; Qiu, F.; Shi, A. C. σ Phase Formed in Conformationally Asymmetric AB-type Block Copolymers. ACS Macro Lett. 2014, 3, 906−910. (18) Liu, M. J.; Qiang, Y. C.; Li, W. H.; Qiu, F.; Shi, A. C. Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers. ACS Macro Lett. 2016, 5, 1167−1171. (19) Lee, W. B.; Elliott, R.; Mezzenga, R.; Fredrickson, G. H. Novel Phase Morphologies in a Microphase-Separated Dendritic Polymer Melt. Macromolecules 2009, 42, 849−859. (20) Gao, Y.; Deng, H. L.; Li, W. H.; Qiu, F.; Shi, A. C. Formation of Nonclassical Ordered Phases of AB-type Multi-arm Block Copolymers. Phys. Rev. Lett. 2016, 116, 068304. (21) Matsen, M. W.; Schick, M. Microphase Separation in Starblock Copolymer Melts. Macromolecules 1994, 27, 6761−6767. (22) Matsen, M. W.; Schick, M. Stable and Unstable Phases of a Linear Multiblock Copolymer Melt. Macromolecules 1994, 27, 7157− 7163. (23) Drolet, F.; Fredrickson, G. H. Combinatorial Screening of Complex Block Copolymer Assembly with Self-Consistent Field Theory. Phys. Rev. Lett. 1999, 83, 4317−4320. (24) Matsen, M. W. Equilibrium Behavior of Asymmetric ABA Triblock Copolymer Melts. J. Chem. Phys. 2000, 113, 5539−5544. (25) Grason, G. M.; Kamien, R. D. Interfaces in Diblocks: A Study of Miktoarm Star Copolymers. Macromolecules 2004, 37, 7371−7380. (26) Nap, R.; Sushko, N.; Erukhimovich, I.; ten Brinke, G. Double Periodic Lamellar-in-Lamellar Structure in Multiblock Copolymer Melts with Competing Length Scales. Macromolecules 2006, 39, 6765−6770. (27) Zhang, L. S.; Lin, J. P.; Lin, S. L. Effect of Molecular Architecture on Phase Behavior of Graft Copolymers. J. Phys. Chem. B 2008, 112, 9720−9728. (28) Wang, L. Q.; Zhang, L. S.; Lin, J. P. Microphase Separation in Multigraft Copolymer Melts Studied by Random-Phase Approximation and Self-Consistent Field Theory. J. Chem. Phys. 2008, 129, 114905.

parameter is the composition. To vary the symmetric composition to be asymmetric offers an opportunity to stabilize the hybrid gyroid−sphere or cylinder−sphere phase. In summary, we have studied the self-assembly behaviors of A1B1A2B2 tetrablock copolymers using SCFT, predicting a stable hybrid lamella−sphere phase. Our results indicate that A1B1A2B2 exhibits significantly different phase behaviors from A1BA2 though similar phase re-entry is observed with both of them. In A1B1A2B2 with symmetric composition, two types of lamellar phases, regular (L) and sandwich-like (L′), are observed, and their transition driven by entropy is identified as first-order. Note that both L′ and LS are formed via the separation of short A2-blocks within B-domain from long A1blocks. Therefore, the formation of L′ at relatively low χN is a prior condition to the formation of LS at high χN because L′ transfers to LS as the disordered A2-blocks locally aggregate into spheres. The stabilization mechanism of L′ as well as LS is explicitly elucidated, and it is found that the tail B2-block plays a critical role. Although the stability region of LS is narrow, on one hand, it could be enlarged by further adjusting the control parameters or optimizing the architecture. On the other hand, the stabilization mechanism of LS is instructive for stabilizing other hybrid phases.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00818. Further description and figures regarding the selfconsistent field theory, the comparisons of free energy, the domain spacing, and so on (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Weihua Li: 0000-0002-5133-0267 An-Chang Shi: 0000-0003-1379-7162 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants Nos 21574026 and 21774025). A.-C. Shi acknowledges the support from the Natural Science and Engineering Research Council (NSERC) of Canada.

■

REFERENCES

(1) Park, M.; Harrison, C.; Chaikin, P. M.; Register, R. A.; Adamson, D. H. Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter. Science 1997, 276, 1401−1404. (2) Bates, F. S.; Fredrickson, G. H. Block Copolymers - Designer Soft Materials. Phys. Today 1999, 52, 32−38. (3) Darling, S. B. Directing the Self-Assembly of Block Copolymers. Prog. Polym. Sci. 2007, 32, 1152−1204. (4) Kim, J. K.; Yang, S. Y.; Lee, Y.; Kim, Y. Functional Nanomaterials Based on Block Copolymer Self-Assembly. Prog. Polym. Sci. 2010, 35, 1325−1343. (5) Li, W. H.; Müller, M. Directed Self-assembly of Block Copolymers by Chemical or Topographical Guiding Patterns: Optimizing Molecular Architecture, Thin-Film Properties, and Kinetics. Prog. Polym. Sci. 2016, 54−55, 47−75. 98

DOI: 10.1021/acsmacrolett.7b00818 ACS Macro Lett. 2018, 7, 95−99

Letter

ACS Macro Letters (29) Wu, Z. Q.; Li, B. H.; Jin, Q. H.; Ding, D. T.; Shi, A. C. Microphase and Macrophase Separations in Binary Blends of Diblock Copolymers. Macromolecules 2011, 44, 1680−1694. (30) Li, W.; Delaney, K. T.; Fredrickson, G. H. Fddd Network Phase in ABA Triblock Copolymer Melts. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 1112−1117. (31) Brown, J. R.; Seo, Y. M.; Sides, S. W.; Hall, L. M. Unique Phase Behavior of Inverse Tapered Block Copolymers: Self- Consistent Field Theory and Molecular Dynamics Simulations. Macromolecules 2017, 50, 5619−5626. (32) Jiang, W. B.; Liu, M. J.; Li, W. H.; Qiu, F.; Shi, A. C. Tetragonal Phase of Cylinders Self-Assembled from Binary Blends of AB Diblock and (A′B)n Star Copolymers. Phys. Chem. Chem. Phys. 2017, 19, 25754−25763. (33) Sakurai, S.; Shirouchi, K.; Munakata, S.; Kurimura, H.; Suzuki, S.; Watanabe, J.; Oda, T.; Shimizu, N.; Tanida, K.; Yamamoto, K. Morphology Reentry with a Change in Degree of Chain Asymmetry in Neat Asymmetric Linear A1BA2 Triblock Copolymers. Macromolecules 2017, 50, 8647−8657. (34) Woloszczuk, S.; Mineart, K. P.; Spontak, R. J.; Banaszak, M. Dual Modes of Self-Assembly in Superstrongly Segregated Bicomponent Triblock Copolymer Melts. Phys. Rev. E 2015, 91, 010601. (35) Masuda, J.; Takano, A.; Nagata, Y.; Noro, A.; Matsushita, Y. Nanophase-Separated Synchronizing Structure with Parallel Double Periodicity from an Undecablock Terpolymer. Phys. Rev. Lett. 2006, 97, 098301. (36) Fleury, G.; Bates, F. S. Perpendicular Lamellae in Parallel Lamellae in a Hierarchical CECEC-P Hexablock Terpolymer. Macromolecules 2009, 42, 1691−1694. (37) (1) The “phase diagram” in block copolymer literature is not a phase diagram in a rigorous sense, but it is commonly used in in the literature. These phase diagrams should be regarded as phase portraits. (2) In our work, we follow the literature and use the term “phase diagram”, but they should be regarded as phase portraits. (3) We thank an anonymous reviewer for pointing this out.

99

DOI: 10.1021/acsmacrolett.7b00818 ACS Macro Lett. 2018, 7, 95−99